Heat oil in a large saucepan over medium heat. Add onion; sauté until softened, 5 minutes. Add garlic; sauté 30 seconds. Stir in tomato; sauté 1 minute.
Add stock, bay leaf and salt. Reduce heat to low. Simmer, uncovered, 10 minutes. Remove from heat. Discard bay leaf. Stir in eggs. Place a slice of bread in each serving bowl and ladle in hot soup. Sprinkle with parsley; serve immediately.